God commanded us to "Give to anyone who asks of us".
So yes, if they are asking, give. It is not your fault what they do with it.
Whether an Orthodox Christian is required to do this is beyond me at this point. It would depend of if an Orthodox Christian takes the bible literally, obeys the commands of God, and doesn't have a canon or some church understanding that allows them to not follow this command.
But what is it that we are expected to give? Read Acts 3. A man was asking for alms, but that's not what Peter and John gave him. What they gave him was what he needed
I disagree (at least at times) with the statement that "it is not your fault". If you give someone something knowing that it will bring him harm, you have done a disservice and ought to be held accountable.
I do agree that we should give requests for assistance their due consideration. However, some wisdom is required as well. Not an easy task.
Also what katherine said above -
We do not know what they'll do with the money. For all we know they could be angels. (unawares).
We all need money for various things. To assume somebody just wants to go buy heroine is judging others.
To assume that I assume that panhandlers just want to go buy heroine is..... what?
They ask for spare change:
It's simple. A quarter, a nickel, and two pennies - floating in your pocket - very simple. Just give.
Yep. Just a toss over a few loose coins. Conscience clear. All is good.
Sometimes a kind word can go a long way, too. Yes, I often give to panhandlers. I will often say something like, "Things are a little tough now?" or "This isn't much, but will it help?" I'm neither Peter nor John so I don't feel qualified to offer everything that might be truly needed, but I try to put a bit of personal touch on it. I usually get a smile in return.
I also frequently contribute to musicians, etc. in public places who have some kind of container for donations. I've even struck up lengthy conversations with some.
People are looking for kindness. It may be money, but not necessarily.